You will find 2 old URL's mysite.se/thepath and mysite.eu/thepath indexed on the internet, but that path does not exist any longer and I must redirect the hyperlinks towards the home page rather : mysite.se for se domain and mysite.eu for eu domain.

As you can tell the website is (joomla) 2 language based and every language is related to a particular domain. And there's just one .htaccess at the bottom from the site.

# If your concerned about direct access to a particular page without the sub-dir # you will want to add something like this
RewriteCond %{REQUEST_URI} ^/thepath
RewriteRule (.*) /$1 [R=301,L]
It was obtained from here